The authors outline a theory of conditionals of the form If A then C and If A then possibly C. The 2 sorts of conditional have separate core meanings that refer to sets of possibilities. Knowledge, pragmatics, and semantics can modulate these meanings. Modulation can add information about temporal and other relations between antecedent and consequent. It can also prevent the construction of possibilities to yield 10 distinct sets of possibilities to which conditionals can refer. The mental representation of a (...) conditional normally makes explicit only the possibilities in which its antecedent is true, yielding other possibilities implicitly. Reasoners tend to focus on the explicit possibilities. The theory predicts the major phenomena of understanding and reasoning with conditionals. (shrink)

In this paper it is argued that, in order to solve the problem of iterated belief change, both the belief state and its input should be represented as epistemic entrenchment (EE) relations. A belief revision operation is constructed that updates a given EE relation to a new one in light of an evidential EE relation. It is shown that the operation in question satisfies generalized versions of the Gärdenfors revision postulates. The account offered is motivated by Spohn's ordinal conditionalization functions, (...) and can be seen as the Jeffrization of a proposal considered by Rott. (shrink)

This paper presents a new theory of the truth conditions for indicative conditionals. The theory allows us to give a fairly unified account of the semantics for indicative and subjunctive conditionals, though there remains a distinction between the two classes. Put simply, the idea behind the theory is that the distinction between the indicative and the subjunctive parallels the distinction between the necessary and the a priori. Since that distinction is best understood formally using the resources of two-dimensional modal logic, (...) those resources will be brought to bear on the logic of conditionals. (shrink)

This paper starts by criticising some olderaccounts of conditionals based on the so-called `Ramsey Test', and ends by proposing their replacement, in part with a material account, in part with a probabilistic account using epsilon terms. The combined replacement is in fact closer to Ramsey's ideas. But there is also a resemblance between the latter and a more recent account of conditionals, which relates some of them to causality. The comparison provides a basis for assessment of the proposed replacement.

Causation is in trouble—at least as it is pictured in current theories in philosophy and in economics as well, where causation is also once again in fashion. In both disciplines the accounts of causality on offer are either modelled too closely on one or another favoured method for hunting causes or on assumptions about the uses to which causal knowledge can be put—generally for predicting the results of our efforts to change the world. The first kind of account supplies no (...) reason to think that causal knowledge, as it is pictured, is of any use; the second supplies no reason to think our best methods will be reliable for establishing causal knowledge. So, if these accounts are all there is to be had, how do we get from method to use? Of what use is knowledge of causal laws that we work so hard to obtain? (shrink)

The Desire-as-Belief thesis (DAB) states that any rational person desires a proposition exactly to the degree that she believes or expects the proposition to be good. Many people take David Lewis to have shown the thesis to be inconsistent with Bayesian decision theory. However, as we show, Lewis's argument was based on an Invariance condition that itself is inconsistent with the (standard formulation of the) version of Bayesian decision theory that he assumed in his arguments against DAB. The aim of (...) this paper is to explore what impact the rejection of Invariance has on the DAB thesis. Without assuming Invariance, we first refute all versions of DAB that entail that there are only two levels of goodness. We next consider two theses according to which rational desires are intimately connected to expectations of (multi-levelled) goodness, and show that these are consistent with Bayesian decision theory as long as we assume that the contents of 'value propositions' are not fixed. We explain why this conclusion is independently plausible, and show how to construct such propositions. (shrink)

The thesis that probabilities of conditionals are conditional probabilities has putatively been refuted many times by so-called ‘triviality results’, although it has also enjoyed a number of resurrections. In this paper I assault it yet again with a new such result. I begin by motivating the thesis and discussing some of the philosophical ramifications of its fluctuating fortunes. I will canvas various reasons, old and new, why the thesis seems plausible, and why we should care about its fate. I will (...) look at some objections to Lewis’s famous triviality results, and thus some reasons for the pursuit of further triviality results. I will generalize Lewis’s results in ways that meet the objections. I will conclude with some reflections on the demise of the thesis—or otherwise. (shrink)

Higginbotham (1986) observed that quantified conditionals have a stronger meaning than might be expected, as attested by the apparent equivalence of examples like No student will pass if he goofs off and Every student will fail if he goofs off. Higginbotham's observation follows straightforwardly given the validity of conditional excluded middle (CEM; as observed by von Fintel & Iatridou 2002), and as such could be taken as evidence thereof (e.g. Williams forthcoming). However, the empirical status of CEM has been disputed, (...) and it is invalid under many prominent theories of conditionals—notably Lewis (1973) for counterfactuals, also Kratzer (1979, 1991). More acutely, Higginbotham's observation holds even for quantified counterparts of conditionals that appear not to obey CEM (Higginbotham 2003), and the standard way of explaining (away) such apparent counterexamples to the principle, à la Stalnaker (1981), does not directly yield an account of our apparent truth-conditional intuitions about the quantified counterparts (Leslie 2009). This article provides an explanation for the latter intuitions within Stalnaker's framework, the upshot being that CEM does remain a viable explanation, in principle, for Higginbotham's observation. (shrink)

This paper discusses and relates two puzzles for indicative conditionals: a puzzle about indeterminacy and a puzzle about triviality. Both puzzles arise because of Ramsey's Observation, which states that the probability of a conditional is equal to the conditional probability of its consequent given its antecedent. The puzzle of indeterminacy is the problem of reconciling this fact about conditionals with the fact that they seem to lack truth values at worlds where their antecedents are false. The puzzle of triviality is (...) the problem of reconciling Ramsey's Observation with various triviality proofs which establish that Ramsey's Observation cannot hold in full generality. In the paper, I argue for a solution to the indeterminacy puzzle and then apply the resulting theory to the triviality puzzle. On the theory I defend, the truth conditions of indicative conditionals are highly context dependent and such that an indicative conditional may be indeterminate in truth value at each possible world throughout some region of logical space and yet still have a nonzero probability throughout that region. (shrink)

This paper is about the situation in which an author (writer or speaker) presents a deductively invalid argument, but the addressee aims at a charitable interpretation and has reason to assume that the author intends to present a valid argument. How can he go about interpreting the author’s reasoning as enthymematically valid? We suggest replacing the usual find-the-missing-premise approaches by an approach based on systematic efforts to ascribe a belief state to the author against the background of which the argument (...) has to be evaluated. The suggested procedure includes rules for recording whether the author in fact accepts or denies the premises and the conclusion, as well as tests for enthymematic validity and strategies for revising belief state ascriptions. Different degrees of interpretive charity can be exercised. This is one reason why the interpretation or reconstruction of an enthymematic argument typically does not result in a unique outcome. (shrink)

This paper explores how the Bayesian program benefits from allowing for objective chance as well as subjective degree of belief. It applies David Lewis’s Principal Principle and David Christensen’s principle of informed preference to defend Howard Raiffa’s appeal to preferences between reference lotteries and scaling lotteries to represent degrees of belief. It goes on to outline the role of objective lotteries in an application of rationality axioms equivalent to the existence of a utility assignment to represent preferences in Savage’s famous (...) omelet example of a rational choice problem. An example motivating causal decision theory illustrates the need for representing subjunctive dependencies to do justice to intuitive examples where epistemic and causal independence come apart. We argue to extend Lewis’s account of chance as a guide to epistemic probability to include De Finetti’s convergence results. We explore Diachronic Dutch book arguments as illustrating commitments for treating transitions as learning experiences. Finally, we explore implications for Martingale convergence results for motivating commitment to objective chances. (shrink)

According to the Ramsey Test hypothesis the conditional claim that if A then B is credible just in case it is credible that B, on the supposition that A. If true the hypothesis helps explain the way in which we evaluate and use ordinary language conditionals. But impossibility results for the Ramsey Test hypothesis in its various forms suggest that it is untenable. In this paper, I argue that these results do not in fact have this implication, on the grounds (...) that similar results can be proved without recourse to the Ramsey test hypothesis. Instead they show that a number of well entrenched principles of rational belief and belief revision do not apply to conditionals. (shrink)

We argue that desire is an attitude that relates a person not to one proposition but rather to two, the first of which we call the object of the desire and the second of which we call the condition of the desire. This view of desire is initially motivated by puzzles about conditional desires. It is not at all obvious how best to draw the distinction between conditional and unconditional desires. In this paper we examine extant attempts to analyse conditional (...) desire. From the failures of those attempts, we draw a moral that leads us to the correct account of conditional desires. We then extend the account of conditional desires to an account of all desires. We attempt to explain the distinction between intrinsic and extrinsic desire in light of our account of desire. We show how to use our account to solve Wollheim’s paradox of democracy and to save modus ponens. Finally, we extend the account of desire to related phenomena, such as conditional promises, intentions, and commands. (shrink)

Prominent instances of anti-luck epistemology, in particular sensitivity and safety accounts of knowledge, introduce a modal condition on the pertinent belief in terms of closeness or similarity of possible worlds. Very roughly speaking, a belief must continue to be true in close possibilities in order to qualify as knowledge. Such closeness-accounts derive much support from their (alleged) ability to eliminate standard instances of epistemic luck as they appear in prominent Gettier-type examples. The article argues that there are new Gettier-type examples (...) which are grounded in “distant” epistemic luck. It is demonstrated that sensitivity and safety theories cannot handle such examples. (shrink)

The so-called ‘Adams’ Thesis’ is often understood as the claim that the assertibility of an indicative conditional equals the corresponding conditional probability—schematically: $${({\rm AT})}\qquad\qquad\quad As(A\rightarrow B)=P({B|A}),{\rm provided}\quad P(A)\neq 0.$$ The Thesis is taken by many to be a touchstone of any theorizing about indicative conditionals. Yet it is unclear exactly what the Thesis is . I suggest some precise statements of it. I then rebut a number of arguments that have been given in its favor. Finally, I offer a new (...) argument against it. I appeal to an old triviality result of mine against ‘Stalnaker’s Thesis’ that the probability of a conditional equals the corresponding conditional probability. I showed that for all finite-ranged probability functions, there are strictly more distinct values of conditional probabilities than there are distinct values of probabilities of conditionals, so they cannot all be paired up as Stalnaker’s Thesis promises. Conditional probabilities are too fine-grained to coincide with probabilities of conditionals across the board. If the assertibilities of conditionals are to coincide with conditional probabilities across the board, then assertibilities must be finer-grained than probabilities. I contend that this is implausible—it is surely the other way round. I generalize this argument to other interpretations of ‘ As ’, including ‘acceptability’ and ‘assentability’. I find it hard to see how any such figure of merit for conditionals can systematically align with the corresponding conditional probabilities. (shrink)

The connection between the probabilities of conditionals and the corresponding conditional probabilities has long been explored in the philosophical literature, but its implementation faces both technical obstacles and objections on empirical grounds. In this paper I ?rst outline the motivation for the probabilistic turn and Lewis’ triviality results, which stand in the way of what would seem to be its most straightforward implementation. I then focus on Richard Jeffrey’s ’random-variable’ approach, which circumvents these problems by giving up the notion that (...) conditionals denote propositions in the usual sense. Even so, however, the random-variable approach makes counterintuitive predictions in simple cases of embedded conditionals. I propose to address this problem by enriching the model with an explicit representation of causal dependencies. The addition of such causal information not only remedies the shortcomings of Jeffrey’s conditional, but also opens up the possibility of a uni?ed probabilistic account of indicative and counterfactual conditionals. (shrink)

In deciding whether to read this paper, it might seem reasonable for you to base your decision on your confidence (i) that, if you read this paper, you will become a better person. It might also seem reasonable for you to base your decision on your confidence (ii) that, if you were to read this paper, you would become a better person. Is there a difference between (i) and (ii)? If so, are you rationally required to base your decision on (...) your confidence in one of the two conditionals, rather than the other? Keith DeRose (2010) proposes a provocative pair of answers to these questions. In this paper, I argue that DeRose’s answers are incorrect, and I defend a rival pair of answers. (shrink)

This paper discusses counterexamples to the thesis that the probabilities of conditionals are conditional probabilities. It is argued that the discrepancy is systematic and predictable, and that conditional probabilities are crucially involved in the apparently deviant interpretations. Furthermore, the examples suggest that such conditionals have a less prominent reading on which their probability is in fact the conditional probability, and that the two readings are related by a simple step of abductive inference. Central to the proposal is a distinction between (...) causal and purely stochastic dependence between variables. (shrink)

Frank Plumpton Ramsey (1903–30) made seminal contributions to philosophy, mathematics and economics. Whilst he was acknowledged as a genius by his contemporaries, some of his most important ideas were not appreciated until decades later; now better appreciated, they continue to bear an influence upon contemporary philosophy. His historic significance was to usher in a new phase of analytic philosophy, which initially built upon the logical atomist doctrines of Bertrand Russell and Ludwig Wittgenstein, raising their ideas to a new level of (...) sophistication, but ultimately he became their successor rather than remain a mere acolyte. (shrink)

I discuss three observations about backtracking counterfactuals not predicted by existing theories, and then motivate a theory of counterfactuals that does predict them. On my theory, counterfactuals quantify over a suitably restricted set of historical possibilities from some contextually relevant past time. I motivate each feature of the theory relevant to predicting our three observations about backtracking counterfactuals. The paper concludes with replies to three potential objections.

I discuss an argument given by Dorothy Edgington for the conclusion that indicative conditionals cannot express propositions. The argument is not effective against Robert Stalnaker's context-dependent propositional theory. I isolate and defend the feature of Stalnaker's theory that allows it to evade the argument.

In this article I offer an approach to counterfactuals based on a notion of objective probability. It is in the spirit of, though it does not fall squarely under, the metalinguistic model. Thus, it is not developed in terms of possible worlds, or notions parasitic on them (e.g., similarity). Its dominant features are rooted in objective probability and causal relevance (analyzed probabilistically), and thus it is not close in spirit to a maximal similarity or a minimal change approach.

Systems of logico-probabilistic reasoning characterize inference from conditional assertions that express high conditional probabilities. In this paper we investigate four prominent LP systems, the systems _O, P_, _Z_, and _QC_. These systems differ in the number of inferences they licence _. LP systems that license more inferences enjoy the possible reward of deriving more true and informative conclusions, but with this possible reward comes the risk of drawing more false or uninformative conclusions. In the first part of the paper, we (...) present the four systems and extend each of them by theorems that allow one to compute almost-tight lower-probability-bounds for the conclusion of an inference, given lower-probability-bounds for its premises. In the second part of the paper, we investigate by means of computer simulations which of the four systems provides the best balance of reward versus risk. Our results suggest that system _Z_ offers the best balance. (shrink)

We prove some embedding theorems for classical conditional logic, covering 'finitely cumulative' logics, 'preferential' logics and what we call 'semi-monotonic' logics. Technical tools called 'partial frames' and 'frame morphisms' in the context of neighborhood semantics are used in the proof.

Conditionals somehow express conditional beliefs. However, conditional belief is a bi-propositional attitude that is generally not truth-evaluable, in contrast to unconditional belief. Therefore, this article opts for an expressivistic semantics for conditionals, grounds this semantics in the arguably most adequate account of conditional belief, that is, ranking theory, and dismisses probability theory for that purpose, because probabilities cannot represent belief. Various expressive options are then explained in terms of ranking theory, with the intention to set out a general interpretive scheme (...) that is able to account for the most variegated usage of conditionals. The Ramsey test is only the first option. Relevance is another, familiar, but little understood item, which comes in several versions. This article adds a further family of expressive options, which is able to subsume also counterfactuals and causal conditionals, and indicates at the end how this family allows for partial recovery of truth conditions for conditionals. (shrink)

6. Seeing With the Mind’s Eye 1: The Puzzle of Mental Imagery .................................................6-1 6.1 What is the puzzle about mental imagery?..............................................................................6-1 6.2 Content, form and substance of representations ......................................................................6-6 6.3 What is responsible for the pattern of results obtained in imagery studies?.................................6-8..

Against Barnett (2012), I argue that the theory I advance in DeRose 2010 is best construed as one on which ‘"were"ed-up’ future-directed conditionals like ‘If the house were not to be painted, it would soon look quite shabby’ are, in ways important to how they function in deliberation, different in literal content from their ‘straightforward’ counterparts like ‘If the house is not painted, it will soon look quite shabby’. I also defend my way of classifying future-directed conditionals against an attack (...) by Barnett by defending a standard (among philosophers) approach to the basic structure of some conditionals. Finally, I counter Barnett’s charge that by using the concept of deliberation in my account of the meaning of future-directed conditionals, I put an implausibly demanding constraint on what it takes to understand such sentences. (shrink)